MATH SOLVE

2 months ago

Q:
# A square prism has a height of 12 inches and a base with an area of 30 square inches. A cylinder is inscribed inside the prism. Which statement about the volume of the cylinder, V, is true?

Accepted Solution

A:

The volume of the cylinder (282.74 in.³) is less than the volume of the square prism (360 in.³). Then the correct option is C.What is a rectangular prism?A rectangular prism is a closed solid that has two parallel rectangular bases connected by a rectangle surface.What is a cylinder?A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.A square prism has a height of 12 inches and a base with an area of 30 square inches.A cylinder is inscribed inside the prism.The volume of the square prism will be[tex]V_{square} =Base[/tex] [tex]area*Height[/tex][tex]V_{square}=30*12[/tex][tex]V_{square} =360[/tex] [tex]in^3[/tex]The volume of the cylinder will be[tex]V_{cylinder}=\pi r^2h[/tex]The radius of the base circle of the cylinder will be[tex]r=\frac{\sqrt[]{30}}{2}[/tex][tex]r=2.7386[/tex]Then volume will be[tex]V_{cylinder}=\pi *(2.7368)^2*12[/tex][tex]V_{cylinder}=282.74[/tex] [tex]in^3[/tex]The volume of the cylinder (282.74 in.³) is less than the volume of the square prism (360 in.³). Then the correct option is C.More about the rectangular prism link is given below.